# Perpendicular Through a Point on a Line

## Explore the construction of a perpendicular line through a point on a line.

Summarize the properties and construction of perpendicular lines, points, and circles. Hint: If you are not familiar with the steps necessary for constructing a perpendicular line through a point on that line, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.

Construct a perpendicular line to line AB through point C by following the construction steps provided below.

## Construction Steps:

 ﻿1. ﻿ Construct another on line AB. (point D) 5.﻿ ﻿ ﻿Construct a circle with the center at point E and radius of g+.5. (circle d) ﻿ ﻿Hint: Be sure to test that when you move point D it stays attached to line AB.﻿ ﻿6. ﻿ Construct a circle with the center at point D and radius of g+.5. (circle e) ﻿﻿2. ﻿ ﻿Construct a circle centered at C and through point D.﻿ (Circle c) ﻿7. ﻿ ﻿Construct the intersection points between circles d & e. (points F & G) ﻿3. ﻿ ﻿Construct the intersection point between circle c and line AB. (point E) 8. ﻿ Construct line GF.﻿ (line h) ﻿4. ﻿ ﻿Construct a segment from point C to D. (segment g) ﻿ ﻿ ﻿You can construct segment EF and FD to explore their relationship.